127 LearnersLast updated on May 29th, 2025
Square of 711
The product of multiplying an integer by itself is the square of a number. Square is used in programming, calculating areas, and so on. In this topic, we will discuss the square of 711.
What is the Square of 711
The square of a number is the product of the number itself.
The square of 711 is 711 × 711.
The square of a number always ends in 0, 1, 4, 5, 6, or 9.
We write it in math as 711², where 711 is the base and 2 is the exponent.
The square of a positive and a negative number is always positive. For example, 5² = 25; -5² = 25.
The square of 711 is 711 × 711 = 505,521.
Square of 711 in exponential form: 711²
Square of 711 in arithmetic form: 711 × 711
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How to Calculate the Value of Square of 711
The square of a number is multiplying the number by itself. So let’s learn how to find the square of a number. These are the common methods used to find the square of a number.
- By Multiplication Method
- Using a Formula (a2)
- Using a Calculator
By the Multiplication method
In this method, we will multiply the number by itself to find the square. The product here is the square of the number. Let’s find the square of 711.
Step 1: Identify the number. Here, the number is 711.
Step 2: Multiplying the number by itself, we get, 711 × 711 = 505,521.
The square of 711 is 505,521.
Using a Formula (a²)
In this method, the formula, a² is used to find the square of the number. Where a is the number.
Step 1: Understanding the equation Square of a number = a²
a² = a × a
Step 2: Identifying the number and substituting the value in the equation.
Here, ‘a’ is 711.
So: 711² = 711 × 711 = 505,521
By Using a Calculator
Using a calculator to find the square of a number is the easiest method. Let’s learn how to use a calculator to find the square of 711.
Step 1: Enter the number in the calculator. Enter 711 in the calculator.
Step 2: Multiply the number by itself using the multiplication button (×). That is 711 × 711
Step 3: Press the equal to button to find the answer. Here, the square of 711 is 505,521.
Tips and Tricks for the Square of 711
Tips and tricks make it easy for students to understand and learn the square of a number. To master the square of a number, these tips and tricks will help students.
- The square of an even number is always an even number. For example, 6² = 36.
- The square of an odd number is always an odd number. For example, 5² = 25.
- The last digit of the square of a number is always 0, 1, 4, 5, 6, or 9.
- If the square root of a number is a fraction or a decimal, then the number is not a perfect square. For example, √1.44 = 1.2.
- The square root of a perfect square is always a whole number. For example, √144 = 12.
Common Mistakes to Avoid When Calculating the Square of 711
Mistakes are common among kids when doing math, especially when it is finding the square of a number. Let’s learn some common mistakes to master the squaring of a number.
Mistake 1
Calculation errors:
Calculation errors mostly happen when students skip the steps or else by swapping the digits. To avoid it, students should double-check the answer. They can double-check by finding the square root of the solution they found.
For example, the square of 25 is 625, and the square root of 625 is ±25.
Mistake 2
Errors while using the formula.
The formula to find the square of the number is a². Instead, students may use 711² with (7+11)² or (700+11)². So students should check and use the correct formula and double-check the answers to avoid all the confusion.
Mistake 3
Confusing square and square root.
Not understanding the concept of square and square root can lead to confusion in students. To avoid it, students should understand the concept that square and square root are inverse operations. The square of 5 is 25 and the square root of 25 is ±5.
Mistake 4
Errors in parentheses.
Ignoring the parentheses when finding the square of a number can lead to errors. So, students should understand parentheses. And do the operations in the correct order to avoid error.
Mistake 5
Not practicing regularly.
Regular practice is required to master the square of a number. So students should do regular practice to avoid errors.
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Solved Examples on Square of 711
Problem 1
Find the side length of a square, where the area of the square is 505,521 cm².
The area of a square = a²
So, the area of a square = 505,521 cm²
So, the side length = √505,521 = 711.
The length of each side = 711 cm
Explanation
The side length of a square is 711 cm.
Because the area is 505,521 cm², the side length is √505,521 = 711.
Problem 2
Sarah wants to tile her square patio of side length 711 feet. The cost of tiling a square foot is 5 dollars. How much will it cost to tile the entire patio?
The side length of the patio = 711 feet
The cost to tile 1 square foot of patio = 5 dollars.
To find the total cost to tile, we find the area of the patio.
Area of the patio = area of the square = a²
Here a = 711
Therefore, the area of the patio = 711² = 711 × 711 = 505,521.
The cost to tile the patio = 505,521 × 5 = 2,527,605.
The total cost = 2,527,605 dollars
Explanation
To find the cost to tile the patio, we multiply the area of the patio by the cost to tile per square foot. So, the total cost is 2,527,605 dollars.
Problem 3
Calculate the area of a circle whose radius is 711 meters.
The area of the circle = 1,588,500.66 m²
Explanation
The area of a circle = πr²
Here, r = 711
Therefore, the area of the circle = π × 711² = 3.14 × 711 × 711 = 1,588,500.66 m².
Problem 4
The area of a square is 505,521 cm². Find the perimeter of the square.
The perimeter of the square is 2,844 cm.
Explanation
The area of the square = a²
Here, the area is 505,521 cm²
The side length is √505,521 = 711
Perimeter of the square = 4a
Here, a = 711
Therefore, the perimeter = 4 × 711 = 2,844.
Problem 5
Find the square of 712.
The square of 712 is 506,944.
Explanation
The square of 712 is multiplying 712 by 712.
So, the square = 712 × 712 = 506,944.
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FAQs on Square of 711
1.What is the square of 711?
2.What is the square root of 711?
3.Is 711 a prime number?
4.What are the first few multiples of 711?
5.What is the square of 710?
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Important Glossary for Square 711.
- Square: The product of multiplying a number by itself.
- Even number: A number divisible by 2. For example, 2, 4, 6, 8, etc. Odd number: A number not divisible by 2. For example, 1, 3, 5, 7, etc.
- Exponential form: The notation of writing a number in the form of a power. For example, 9² where 9 is the base and 2 is the power.
- Perfect square: A number that is the square of an integer. For example, 36 is a perfect square because it is 6².
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Jaskaran Singh Saluja
About the Author
Jaskaran Singh Saluja is a math wizard with nearly three years of experience as a math teacher. His expertise is in algebra, so he can make algebra classes interesting by turning tricky equations into simple puzzles.
Fun Fact
: He loves to play the quiz with kids through algebra to make kids love it.
